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Are the colors 0026FF and 8026FF the same?

No, they are not. And the difference between blue (0026FF) and purple (8026FF) is a 1 bit error.

You will see an image, but not the image your DVD told your TV to display.

edit: This comment makes a lot less sense with the deleted comment removed.

It takes a lot of noise to alter the digital signal like this. If we're talking long distance, like a telephone line, the signal gets weak enough that it can happen regularly, but on the cable from the DVD to the TV the voltage drop is ridiculously low. Noise doesn't affect your signal by 4 volts unless you have a serious problem with your system.

Actually, I think that it takes the exact same amount of noise to flip a bit as it does to transmit a bit.

Through the principle of superposition, if you transmit a 0 with X watts, and I transmit a 1 with X watts, our combined signal will be somewhere in the middle, which can cause a bit flip.

I am not talking about voltage drop from end to end, which is a separate issue. I am talking about interference occurring adjacent to any point on the cable that you pick.

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